With the stencils in Tables REF , REF  and the corresponding locations in Table REF , one can do the classical symmetric Gauss-Seidel including the symmetric red-black Gauss-Seidel iteration (shorten as SRBGS henceforth) conveniently [1]}, [2]}. To do SRBGS iteratons, one should mark all points as red or black points first. For example, let \(\Omega _{red}: =\lbrace (i,j) \in \Omega | i+j \ \text{even} \rbrace \)  and \(\Omega _{black}: =\lbrace (i,j) \in \Omega | i+j \ \text{odd} \rbrace \) . Then one can first update all the red points with the five-point stencils in Table REF  or REF  using all the black neighbor points followed by updating all the black points with the five-point stencils in Table REF  or REF  with the updated red neighbor points. Finally, update all the red points again. Then the one cycle Gauss-Seidel iterations with updating order “red \(\rightarrow \)  black \(\rightarrow \)  red" is finished and it is called one time SRBGS iteration. For more details of the SRBGS, we refer to [3]} (section 4.1.3). Henceforth, we will use the following notation to denote the \(n\)  times SRBGS iterations for the equation (REF )
with initial iteration value \(u^0\)
\(\text{SRBGS}(\gamma (x), d^1, d^2, z, u^0, n),\) 
